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The following data represent the number of calories per serving and the number of grams of sugar per serving for a random sample of high-fiber cereals. Complete parts (a) through (d) below. Calories, x 210 230 180 160 220 Q 20+ Q sugar Sugar, y 17 16 17 13 50 250 calories Click the icon to view the table of critical values of the correlation coefficient. (a) A scatter diagram of the data is shown. What type of relation appears to exist between calories and sugar content? O A. There appears to be a strong nonlinear relationship between calories and sugar content. O B. There appears to be a strong linear relationship between calories and sugar content. C. There appears to be little or no relationship between calories and sugar content. X (b) Determine the correlation coefficient between calories and sugar content Table of Critical Values of the Correlation Coefficient The correlation coefficient is - 0.615 . (Type an integer or decimal rounded to three decimal places as needed.) Determine the critical value for the correlation coefficient. 0.997 0.95 0.878 0.878 (Type an integer or decimal rounded to three decimal places as needed.) 0.811 Is there a linear relation between calories and sugar content? 0.754 0.70 O A. Since the absolute value of the correlation coefficient is less than the critical value, there is a linear relation between calories and sugar content. 0.666 B. Since the absolute value of the correlation coefficient is greater than the critical value, there is not a linear relation between calories and sugar content. 0.632 C. Since the absolute value of th 0.602 ficient is less than the critical value, there is not a linear relation between calories and sugar content. 0.576 D. Since the absolute value of the coefficient is greater than the critical value, there is a linear relation between calories and sugar content. 0.553 0.532 (c) Suppose that we add another cereal, which has 50 calories and 3 grams of sugar per serving, to the data set. Redraw the scatter diagram of the data with this cereal included. Choose the correct plot below. 0.514 OB. 0.49 0.48 20- 250- 0.468 . . 0.456 suga calorie 0.444 sugar 250 calories sugar 50 250 Print Done calories Recompute the correlation coefficient. The new correlation coefficient is. (Type an integer or decimal rounded to three decimal places as needed.) Help Me Solve This View an Example Get More Help - Clear All Check Answer2 A professor feels that there is a relation between the number of hours a statistics student studies each week and the student's age. She conducts a survey in which 26 statistics students are asked their age and the number of hours they study statistics each week. She obtains the accompanying results. Complete parts (a) through (e). a Click the icon to view the data table. (a) Draw a scatter diagram of the data. Choose the correct graph below. V A' ' B' Data Table ' Q E 2- 5 Hours Hours Hours m D m Age, X Studying, y x Studying, y Age, x Studying, y 18 4.2 5.1 22 2.1 18 1 .1 2.3 22 3.6 Determine any potential inuential observations. Choose the correct answer below. :2 3': 25': :2 j: A_ (13,\") 1a 5.3 3.2 25 3.9 V 18 3.2 5.3 26 5.2 ' 5' (35'8'3) 19 2.3 2.5 26 4.2 c. (20,62) and (2115.3) 19 2.3 6.3 35 3.3 D. There are no potential inuential observations. 19 3.2 4.2 (b) Find the least-squares regression line using all the data points. Choose the correct answer below. 9= 0.239x+ - 1.05) (Round the splope to three decimal places as needed. Round the intercept to two decimal places as needed.) (c) Find the least-squares regression line with the data point (35.8.3) removed. Choose the correct answer below. 9= x + | (Round the splope to three decimal places as needed. Round the intercept to two decimal places as needed.) Help Me Solve This View an Example Get More Help A Clear All 3 Is the width of a tornado related to the amount of distance for which the tornado is on the ground? The accompanying data represent the width (yards) and length (miles) of tornadoes in a particular region for one calendar year. Complete parts (a) through (n) below. Click the icon to view the tornado data. (a) What is the explanatory variable? X Tornado Data O Length Width Width (yd) Length (mi) Width (yd) Length (mi) Width (yd) Length (mi) (b) Explain why this data should be analyzed as bivariate quantitative data. 50 1.3 1960 16.6 50 0.1 660 B.2 30 0.8 10 0.8 For each tornado, two quantitative variables are measured: width and length. 220 0.9 200 4.1 190 2.5 480 5.8 (c) Draw a scatter diagram of the data. What type of relation appears to exist between the width and length of a tornado? Choose the correct scatter diagram below. 160 0.6 480 6.5 110 3.4 360 4.3 50 1.2 O B. O C. 230 5.5 560 5.7 30 0.4 60 0.5 1.3 2000 19.3 25- 110 25- 260 1.4 880 9.1 120 0.4 400 2.2 600 11.2 320 0.5 Length Length 170 50 0.1 Length 120 0.9 1.5 130 1.8 270 2.9 130 5.1 2000 200 2.1 450 9.9 210 2.8 2000 2000 Width Width 100 7.5 230 5.4 220 1.5 Width 330 2.9 290 0 .6 590 6.7 770 8.8 500 6.9 50 0.6 There is a positive relationship between the width and length of a tornado. 50 0.1 20 0.8 350 1.3 (d) Determine the correlation coefficient between width and length. 40 0.1 20 190 0.5 0.1 20 0.2 110 0.9 r= 20 0.1 10 0.1 50 0.2 (Round to three decimal places as needed.) 40 0.5 150 0.9 310 0.9 970 4.4 90 0.3 360 4.1 190 0.5 110 0.7 380 4.7 1230 19.7 200 1.6 470 1.5 1400 22.6 760 8.2 870 3.3 30 2.2 60 0.4 0.1 50 0.2 50 0.1 0.1 510 7.8 210 0.4 660 10.9 50 01 Print Done Clear All Check Answer Help Me Solve This View an Example Get More Help -4 What is the coefficient of determination for Data Set B? The coefficient of determination for Data Set B is %. Full Data Set: (Type an integer or decimal rounded to the nearest tenth as needed.) Data Set A Data Set B Data Set C X X 3.6 8.9 3.1 8.9 2.8 8.9 8.3 15.0 9.4 15.0 8.1 15.0 0.5 4.8 1.2 4.8 3.0 4.8 1.4 6.0 1.0 6.0 8.3 6.0 8.2 14.9 9.0 14.9 8.2 14.9 5.9 11.9 5.0 1.9 1.4 11.9 4.3 9.8 3.4 9.8 1.0 9.8 8.3 15.0 7.4 15.0 7.9 15.0 0.3 4.7 0.1 4.7 5.9 4.7 6.8 13.0 7.5 13.0 5.0 13.0 (This is a reading assessment question. Be certain of your answer because you only get one attempt on this question.) Textbook StatCrunch Get More Help - Clear All Check Answer5 A probability experiment is conducted in which the sample space of the experiment is S = {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}, event F= {7, 8, 9, 10, 11}, and event G= {11, 12, 13, 14). Assume that each outcome is equally likely. List the outcomes in F or G. Find P(F or G) by counting the number of outcomes in F or G. Determine P(F or G) using the general addition rule. List the outcomes in F or G. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. For G= { 7,8,9,10, 11, 12, 13, 14 } (Use a comma to separate answers as needed.) O B. For G= { } Find P(F or G) by counting the number of outcomes in F or G. (F or G) = (Type an integer or a decimal rounded to three decimal places as needed.) Help Me Solve This View an Example Get More Help - Clear All Check Answer6 A probabllily experiment Is conducted In which the sample space of the experiment Is S =(4,5,6,7,8,9,10,11,12,13,14,15). Let event E = (7,8,9,10}. Assume each outcome ls equally likely. Llsl the outcomes In E\". Flnd P (E\") . List the outcomes in Et Select the correct choice beluw and. if necessary, ll in the answer box to complete your choice 'A- E\" = {4.5.6.11.12.13.14.15} (Use a comma to separate answers as needed.) 5- E =r) P (EC) = (Type an integer or a decimal rounded to three decimal places as needed) Help Me Solve This View an Example Get More Help A Clear All 7 The data on the right represent the number of live multiple-delivery births (three or more babies) in a particular year for women 15 to 54 years old Use the data to complete parts (a) through (d) below. Number of Multiple '27 Age Birth: 1 51 9 89 20-24 503 25-29 1629 3034 2829 3539 1844 40-44 375 4564 1 16 (9) Determine the probability that a randomly selected multiple birth for women 15-54 years old involved a mother 30 to 39 years old. mo to 39): 0,633 (Type an integer or decimal rounded to three decimal places as needed) (h) Determine the probability that a randomly selected multiple birth tor women 15-54 years old involved a mother who was not 30 to 39 years old. P(not so to 39)= 0.367 (Type an integer or decimal rounded to three decimal places as needed.) (c) Determine the probability that a randomly selected multiple birth for women 15-54 years old involved a mother who was less than 45 years old P(Iess than 45) = (Type an integer or decimal rounded to three decimal places as needed.) Help Me Solve This View an Example Get More Help A Clear All ' Check Answer 8 For a parallel stmcture of identical components. the system can succeed if at least one of the components succeeds. Assume that components fail independentty at each other and that each component has a 0.16 probability of failure. Complete parts (a) through (0) below. (3) Would it be unusual to observe one component fail? Two components? It i be unusual to observe one component fail. since the probability that one component tails. , is V than 0.05. M V be unusual to observe two components tail, since the probability thattwo components tail. , is V than 0.05. (Type integers or decimals. Do not round.) \"would\" or \"would not\" \"greater" or \"less\" \"would\" or \"would not\" \"greater" or \"less\" Help Me Solve This View an Example Get More Help A Clear All CO Suppose the data to the right represent the survival data for the a certain ship that sank. The males are adult males and the females are adult females. Complete parts (a) through (j). e Female Child Total Survived 272 474 66 812 Died 1,433 153 51 1,637 Total 1,705 627 117 2,449 (a) If a passenger is selected at random, what is the probability that the passenger survived? 0.332 (Round to three decimal places as needed.) (b) If a passenger is selected at random, what is the probability that the passenger was female? 0.256 (Round to three decimal places as needed.) (c) If a passenger is selected at random, what is the probability that the passenger was female or a child? 0.304 (Round to three decimal places as needed.) (d) If a passenger is selected at random, what is the probability that the passenger was female and survived? 0.194 (Round to three decimal places as needed.) (e) If a passenger is selected at random, what is the probability that the passenger was female or survived? 0.394 (Round to three decimal places as needed.) (f) If a female passenger is selected at random, what is the probability that she survived? 0.756 (Round to three decimal places as needed.) (g) If a child passenger is selected at random, what is the probability that the child survived? 0.564 (Round to three decimal places as needed.) (h) If a male passenger is selected at random, what is the probability that he survived? 0.160 (Round to three decimal places as needed.) (i) Do you think the adage "women and children first" was adhered to on this ship? O A. No, because the survival rate for men was about the same as the survival rates for women and children. B. Yes, because the survival rate for men was much lower than the survival rates for women and children. O C. No, because the survival rate for men was higher than the survival rates for women and children. (j) Suppose two females are randomly selected. What is the probability both survived? (Round to four decimal places as needed.) 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